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All of these groups with a possible exception of $2.\\mathfrak{A}_6$ and $6.\\mathfrak{A}_6$ indeed act on some rationally connected threefolds."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.09226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-24T21:13:29Z","cross_cats_sorted":[],"title_canon_sha256":"aec54371c145db708b80c56c3f4eb0b30719f31c0c66c44e004fb37f7bbc9722","abstract_canon_sha256":"7504c9c10b57f0b3740dc27385e57c4d77b1735b95a78d73c783224999f99cc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:53.994813Z","signature_b64":"nN+UEIaCAEi8mRDLUtPDtWN3Mm0UW5VqJFEE5lbOJd/c+qXSJvSs40oLZ5bumw8idXsWBhczu3w1+7FRN1ELAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0b2d5ddfcfa81145cc0974a537eb875719d9d0a795f9615dcc0d8f22a3975bf","last_reissued_at":"2026-05-18T00:04:53.994295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:53.994295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite quasisimple groups acting on rationally connected threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander Duncan, Ivan Cheltsov, J\\'er\\'emy Blanc, Yuri Prokhorov","submitted_at":"2018-09-24T21:13:29Z","abstract_excerpt":"We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: $\\mathfrak{A}_5$, $\\operatorname{PSL}_2(\\mathbf{F}_7)$, $\\mathfrak{A}_6$, $\\operatorname{SL}_2(\\mathbf{F}_8)$, $\\mathfrak{A}_7$, $\\operatorname{PSp}_4(\\mathbf{F}_3)$, $\\operatorname{SL}_2(\\mathbf{F}_{7})$, $2.\\mathfrak{A}_5$, $2.\\mathfrak{A}_6$, $3.\\mathfrak{A}_6$ or $6.\\mathfrak{A}_6$. All of these groups with a possible exception of $2.\\mathfrak{A}_6$ and $6.\\mathfrak{A}_6$ indeed act on some rationally connected threefolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09226","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.09226","created_at":"2026-05-18T00:04:53.994383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.09226v1","created_at":"2026-05-18T00:04:53.994383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09226","created_at":"2026-05-18T00:04:53.994383+00:00"},{"alias_kind":"pith_short_12","alias_value":"4CZNLXP47KAR","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4CZNLXP47KARIXGA","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4CZNLXP4","created_at":"2026-05-18T12:32:05.422762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV","json":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV.json","graph_json":"https://pith.science/api/pith-number/4CZNLXP47KARIXGAS5FFG7VYOV/graph.json","events_json":"https://pith.science/api/pith-number/4CZNLXP47KARIXGAS5FFG7VYOV/events.json","paper":"https://pith.science/paper/4CZNLXP4"},"agent_actions":{"view_html":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV","download_json":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV.json","view_paper":"https://pith.science/paper/4CZNLXP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.09226&json=true","fetch_graph":"https://pith.science/api/pith-number/4CZNLXP47KARIXGAS5FFG7VYOV/graph.json","fetch_events":"https://pith.science/api/pith-number/4CZNLXP47KARIXGAS5FFG7VYOV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV/action/storage_attestation","attest_author":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV/action/author_attestation","sign_citation":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV/action/citation_signature","submit_replication":"https://pith.science/pith/4CZNLXP47KARIXGAS5FFG7VYOV/action/replication_record"}},"created_at":"2026-05-18T00:04:53.994383+00:00","updated_at":"2026-05-18T00:04:53.994383+00:00"}